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Lesson: Properties of Rhombuses

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

Given that 𝐴 𝐡 𝐢 𝐷 is a rhombus with π‘š ∠ 𝐷 𝐡 𝐢 = 4 9 ∘ , what is π‘š ∠ 𝐷 𝐴 𝐡 ?

  • A 8 2 ∘
  • B 4 9 ∘
  • C 7 7 ∘
  • D 1 3 1 ∘

Q2:

is a rhombus. If , find the value of .

  • A34
  • B4
  • C79
  • D56
  • E11

Q3:

In a rhombus , and . Find the value of .

  • A5
  • B18
  • C9
  • D8
  • E13

Q4:

Choose from the following statements the properties of a rhombus.

  1. It has four right angles.
  2. It has two pairs of angles equal in measure.
  3. It has only one pair of parallel sides.
  4. It is a parallelogram of four sides of equal length.
  5. It is a parallelogram of four equal angles.
  • AB and D
  • BD and E
  • CA and B
  • DB and E
  • EB and C

Q5:

If 𝐴 𝐡 𝐢 𝐷 is a rhombus, which line is the perpendicular bisector of 𝐴 𝐢 ?

  • A βƒ–     βƒ— 𝐡 𝐷
  • B βƒ–     βƒ— 𝐴 𝐡
  • C βƒ–     βƒ— 𝐢 𝐷
  • D βƒ–      βƒ— 𝐴 𝐷

Q6:

Are the opposite sides of a rhombus parallel?

  • A No
  • B Yes

Q7:

Do the two diagonals of a rectangle and a rhombus bisect each other?

  • Ano
  • Byes

Q8:

Determine whether this statement is true or false: All rhombuses are regular polygons.

  • Atrue
  • Bfalse

Q9:

Which of the following statements is NOT true for ALL rhombuses?

  • AIt is a parallelogram with 4 right angles.
  • BIt is a quadrilateral of sides equal in length.
  • CIt is an equilateral polygon.
  • DIt has 2 pairs of parallel lines.
  • EIt has 2 pairs of angles equal in measure.

Q10:

Determine the sizes of and in the rhombus .

  • A ,
  • B ,
  • C ,
  • D ,

Q11:

In the given rhombus 𝐴 𝐡 𝐢 𝐷 , 𝐷 𝐡 = 6 π‘₯ βˆ’ 8 and 𝑃 𝐡 = 2 π‘₯ + 9 . Find the length of 𝑃 𝐷 .

Q12:

The figure shows rhombus 𝐴 𝐡 𝐢 𝐷 . Find π‘š ∠ 𝐡 𝐴 𝐢 and the length of 𝐴 𝐷 .

  • A 6 0 ∘ , 29 cm
  • B 6 0 ∘ , 14.5 cm
  • C 3 0 ∘ , 14.5 cm
  • D 3 0 ∘ , 29 cm

Q13:

In the given rhombus , . Find .

  • A
  • B
  • C
  • D
  • E

Q14:

𝐴 𝐡 𝐢 𝐷 is a quadrilateral. The coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( 1 , 2 ) , ( βˆ’ 7 , 1 ) , and ( 0 , βˆ’ 3 ) respectively. Find the coordinates of point 𝐷 if the figure is a rhombus.

  • A ( 8 , βˆ’ 2 )
  • B ( 9 , βˆ’ 4 )
  • C ( 1 3 , 2 )
  • D ( 8 , βˆ’ 7 )

Q15:

Determine the perimeter of the rhombus 𝐴 𝐡 𝐢 𝐷 , given that the points 𝐴 and 𝐡 are ( βˆ’ 5 , βˆ’ 1 ) and ( βˆ’ 4 , 4 ) .

  • A 4 √ 2 6 length units
  • B √ 2 6 length units
  • C 2 √ 3 length units
  • D26 length units

Q16:

Given that the points 𝐴 ( βˆ’ 3 , 3 ) , 𝐡 ( 2 , βˆ’ 4 ) , 𝐢 ( 9 , βˆ’ 9 ) , and 𝐷 ( 4 , βˆ’ 2 ) are vertices of the rhombus 𝐴 𝐡 𝐢 𝐷 , find the coordinates of the point of intersection of its two diagonals.

  • A ( 3 , βˆ’ 3 )
  • B ( βˆ’ 6 , 6 )
  • C ( βˆ’ 3 , 3 )
  • D ( 0 , 0 )

Q17:

The figure shows a rhombus. Given that π‘š ∠ 𝐴 𝑀 𝐻 = 5 0 ∘ , what are the measures of the angles at 𝐴 , 𝐡 , 𝐢 , and 𝐷 ?

  • A 8 0 ∘ , 1 0 0 ∘ , 8 0 ∘ , and 1 0 0 ∘
  • B 4 0 ∘ , 5 0 ∘ , 4 0 ∘ , and 5 0 ∘
  • C 4 0 ∘ , 1 4 0 ∘ , 4 0 ∘ , and 1 4 0 ∘
  • D 9 0 ∘ , 1 0 0 ∘ , 9 0 ∘ , and 8 0 ∘

Q18:

Is the following statement true or false? In a rhombus, all sides are equal in length.

  • Afalse
  • Btrue

Q19:

Are the sides of a rhombus equal in length?

  • Ano
  • Byes

Q20:

Are the two diagonals of a rhombus perpendicular?

  • Ano
  • Byes

Q21:

Determine whether the following sentence is true or false: A rhombus has only one pair of parallel sides.

  • A true
  • B false

Q22:

In the rhombus shown, determine π‘š ∠ 𝑋 , π‘š ∠ π‘Œ , π‘š ∠ 𝑍 , and π‘š ∠ 𝐿 .

  • A 9 4 ∘ , 8 6 ∘ , 9 4 ∘ , 8 6 ∘
  • B 1 3 7 ∘ , 4 3 ∘ , 1 3 7 ∘ , 4 3 ∘
  • C 4 3 ∘ , 8 6 ∘ , 1 3 7 ∘ , 9 4 ∘
  • D 9 0 ∘ , 8 6 ∘ , 9 0 ∘ , 9 4 ∘

Q23:

Are the angles in a rhombus right angles?

  • Ayes
  • Bno

Q24:

In which of these quadrilaterals are the diagonals perpendicular but not equal in length?

  • Arhombus
  • Btrapezium
  • Crectangle
  • Dsquare

Q25:

A rhombus is a square if its are equal in length.

  • Asides
  • Bdiagonals
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